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Mathematical Methods

Mathematical Methods of Operations Research (ZOR)
Publisher: Physica Verlag, An Imprint of Springer-Verlag GmbH
ISSN: 1432-2994 (Paper) 1432-5217 (Online)
Issue: Volume 46, Number 3
Date:  December 1997
 math_meth

Solving Stochastic Structural Optimization Problems by RSM-Based Stochastic Approximation Methods – Gradient Estimation in Case of Intermediate Variables


Abstract:

Reliability-based structural optimization methods use mostly the following basic design criteria: I) Minimum weight (volume or costs) and II) high strength of the strucure. Since several parameters of the structure, e.g. material parameters, loads, manufacturing errors, are not given, fixed quantities, but random variables having a certain probability distribution P, stochastic optimization problems results from criteria (I), (II), which can be represented by $$min_{x\in D} F(x) with F(x):= Ef(\omega,x). (1)$$

 

Here, f=f(P, x) is a function on Ÿr depending on a random element P, “E” denotes the expectation operator and D is a given closed, convex subset of Ÿr. Stochastic approximation methods are considered for solving (1), where gradient estimators are obtained by means of the response surface methodology (RSM). Moreover, improvements of the RSM-gradient estimator by using “intermediate” or “intervening” variables are examined.


Keywords:

  • Reliability-based structural optimization
  • Stochastic optimization
  • Stochastic approximation
  • Response surface method
  • Intermediate variables